On an equivalent representation of the Green's function for the Helmholtz problem in a non-absorbing impedance half-plane

The Green's function associated with the Helmholtz problem in a non-absorbing impedance half-plane can be expressed as an integral form. In the non-absorbing case, the presence of surface waves presents a challenge in order to obtain accurate approximations. In this work, we present an equivalent representation for this Green's function, expressed as a sum of analytical terms and bounded integrals. The resulting representation is numerically stable and it can be estimated by any well known robust integration rule for bounded intervals. We provide a detailed description of the equivalent representation and we validate it with numerical experimentation.